This study examines the strong and weak convergence of the F ∗ iterative approach to the fixed point of a nonexpansive mapping in the context of a Banach space. This work shows improved rate and efficiency of convergence. Furthermore, we proved that F ∗ iterative algorithm converges to a fixed point faster than Picard, Mann, S, and Varat iterative algorithms. Finally, we provide numerical examples to support the main results and provide numerical and graphical representations through MATLAB.
Panwar et al. (2026) studied this question.